IR optical absorption in doped GaAs

[ondracka]

Dear EPW users and developers,

I'm looking for some help and feedback regarding calculations of optical absorption for p-doped GaAs (5e17 concentration). For most parts I was closely following the "Phonon-assisted optical absorption with EPW" tutorial session from 2024 School, with (hopefully) appropriate adaptations for GaAs.

I'm using QE with PBE and spin orbit coupling for the ground state and phonons with 12x12x12 k-grid and 6x6x6 q-grid, and for the EPW calculations I'm using energies from a PBE0 hybrid run. My motivation is to try to look into IR range absorption where I have some experimental dielectric function available, specifically, I see a broad absorption in the range 0.2-0.6eV with two minor bumps (features (~0.29 and 0.36eV)), see the attached figure. Interestingly, the energy difference of those 2 features is approximately 2 times the energy of TO phonons which is what motivated me to see if I can reproduce something like this with EPW.

What works up to now:
- wannierization looks fine, the wannier band structure seems a good match for the underlying DFT hybrid run.
- I can get the direct optical transitions just fine. The convergence requirements are brutal (over 100x100x100 k-point grid is needed), but still easily doable for the direct transitions. In general the spectra matches well the experimental one, see the attached figure. The discrepancies are shifts related to issues of the hybrid band structure not EPW, specifically the predicted energy difference between the VBM and the split off band bellow is larger in the hybrid than in experiment and I don't see the light-holes heavy-holes transitions experimentally which corresponds to the predicted absorption below 0.3eV (in the experiment the Drude term is already too strong to see the interband transition in that region. However, importantly I don't get any of those weak features that I see in the experiment (~0.29 and 0.36eV), but that could just mean they are not related to direct transitions...

What doesn't work:
- the symetry is broken quite a lot for the direct transitions, the difference between the xx, yy and zz dielectric tensor components can be up to 50%. Quantum espresso runs are using proper symmetry and I'm using also mp_mesh_k = .true. for EPW, so I wonder at which point the symmetry breaks? Is this from the Wannierization? In general the average dielectric function looks fine (even the absolute intensity is a really good match for the experimental dielectric function), so just want to make sure this is not something signalling some deeper issue.
- The indirect transitions are probably impossible to really converge at least based on my current testing and CPU limitations. The best I did was 48x48x48 k-points with 24x24x24 q-points, and that took around 10k core hours. I could probably afford an order of magnitude longer run, but with the k-point * q-point scaling I don't think it would get me much closer to the convergence to be really worth it. I don't see anything resembling the spectral features I'm looking for in the indirect spectra, but as I said its not much converged so who knows. That said, in the theory manuscript [1] the discussion is mostly focusing on the relative intensities of the contributions (there seems to be some features in the indirect "phonon" spectra in FIG. 2 as well, most notably some small peak between 1 and 2 μm in 2(a) also small oscillations in the same region in the 2(b), but they are not discussed AFAICS so I'm assuming they can be also convergence artifacts). Now the tricky part from my current understanding is that the intensity of the indirect transitions depend on the η broadening parameter - a shortcoming which comes directly from the theory. In the tutorial just the ε2|η=0.1eV is shown, while in the [1] 2*ε2|η=0.2eV - ε2|η=0.1eV formula is used in [1] and it references [2]. The referenced ACS Nano paper has a bit of discussion about the reason for the subtraction (cancellation of the diverging term), but for the specific used value of η=0.1eV it just links to the the indirect Si transitions paper [3], but that one has just offhand comment that it was set to a constant value (100 meV) but it doesn't matter in that spectra region (there are no overlapping direct transitions). Now what is a bit problematic is that if I actually use the same 2*ε2|η=0.2eV - ε2|η=0.1eV formula, I'm getting a negative ε2 in some spectral range (~0.4-0.7eV which is most of the range where the relevant direct transitions are).

Therefore my main question is, can I find somewhere some more extensive explanation of the η=0.1eV value or is this mostly just empirical (as it now seems to be from my current reading of the manuscripts)? Additionally, if I disregard the negative ε2, in the other parts of the IR spectra the indirect transitions are maybe 10x weaker than the direct ones, would it still be reasonable to make the claim that the visible features are not phonon-assisted transitions, based just on the predicted magnitude of the (non-completelly converged) indirect absorption with the η=0.1eV value? That however still leaves the question where the features comes from. Could he issue of the hybrid (I could probably try GW) or could excitons still be a thing in this spectral range and doping concentrations? But thats obviously beyond the scope of this forum...

Figure with the dielectric function, QE and epw inputs and some relevant outputs are attached.

Best regards
Pavel Ondračka
Department of Plasma Physics and Technology
Masaryk University, Brno, Czechia

P.S.: I was not sure about the right forum section for this post, there are some technical questions as well as some more theoretical, so hopefully "running the code" is the correct one.

[1] "Ab initio theory of free-carrier absorption in semiconductors" PHYSICAL REVIEW B 106, 205203 (2022)
[2] "Nonradiative Plasmon Decay and Hot Carrier Dynamics: Effects of Phonons, Surfaces, and Geometry" ACS Nano 2016, 10, 957−966
[3] "Phonon-Assisted Optical Absorption in Silicon from First Principles" PRL 108, 167402 (2012)